We prove Shao and Yu�s tightness criterion for the generalized empirical process in the space ??[0, 1] with ??1 topology. Covariance\r\ninequalities are used in applying the criterion to particular types of the empirical processes.We weaken the assumptions imposed\r\non the covariance structure as well as the properties of the underlying sequence of r.v.�s, under which presented processes converge\r\nweakly.
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